STUDY OF INTERPLY SLIP DURING THERMOFORMING OF CONTINOUS FIBER - - PDF document

18TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS

1 General Introduction Continuous fiber thermoplastic composites have been introduced as structural materials for aerospace and automotive applications [1, 2, 3]. Thermoplastics are characterized by their plasticity at high temperature and their rigidity after forming. In recent years, a large number of manufacturing processes have been developed while existing ones were modified in order to obtain a high quality

• process. The stamp forming process is generally

chosen to process consolidated composite plates [4], consolidation, including void reduction and elimination, appears to be an important step before forming. During forming of a pre-consolidated laminate, the individual plies slide over each other to avoid wrinkling [4 ,5, 6, 7, 8, 9]. The constraints imposed by friction between subsequent plies and between the laminate and the tools are major factor in the laminate deformations generated during composite forming. In this work, a model was developed that predicts the friction between subsequent plies. The model is based on the Reynolds’ equation for thin film lubrication and assumes hydrodynamic lubrication

• n a meso-mechanical level.

1.1 Review Various studies have been performed on interply friction of woven-fabric composites [6, 10]. Some studies showed that the friction coefficient is related to the Hersey number, H, which is function of viscosity, , velocity, U, and normal force, N.

U H N η =

(1)

Another approach was presented by Akkerman and

• al. [9] that predicts friction between thermoplastic

laminates and a rigid tool by assuming hydrodynamic lubrication on a meso-mechanical level. The film thickness was derived iteratively from the Reynolds’ equation for thin film lubrication. The fabric geometry and the matrix materials were used as the input parameters. 2 Friction model A new model was developed to simulate the ply-ply

• friction. Fig.1 presents a schematic representation of

to plies separated by a matrix film. Fig.1. Schematic representation of two subsequent plies It is assumed that the equation governing the flow between those plies is the incompressible, stationary Reynolds equation which for the two dimensional state reads:

( )

3 3 2 2 1 2 1 2 2 1 1 2

3 3 ( ) 0, 12 2 h h h h h h h h div grad P V η

→

• −

− + +

• −

=

• (2)

P is the pressure, (h1-h2) the local film thickness, the viscosity and V is the slip velocity.

1 2 3 4 5 6 2 4 6 0.4 0.6 0.8 1 1.2 1.4 1.6 x 10

• 3

x (cm) y (cm) Z(x,y) (cm)

Z (x,y) y x Tx Ty h2 (x,y) h1 (x,y) Moving ply Fixed ply

STUDY OF INTERPLY SLIP DURING THERMOFORMING OF CONTINOUS FIBER COMPOSITE MATERIALS

• E. Gazo-Hanna1, A. Poitou1, P. Casari1, L. Juras2

1 GeM, Ecole Centrale de Nantes, Nantes, France, 2 Cetim de Nantes, Nantes, France

Keywords: friction, thermoplastic, forming, interply slip

This equation describes the relation between the pressure and thickness distribution of a Newtonian fluid matrix. The resolution of (equ. 2) is usually made using a finite element method. In our case and considering a periodic profile for h1(x,y) and h2(x,y), a pseudo spectral method could be used. One boundary condition is needed. (0,0) P = (3) It’s important to notice through the writing of the Reynolds equation that the pressure depends linearly

• n velocity. For this reason, we will try first, and

using method described above to solve the Reynolds equation for two different cases where in the first

• ne, the moving ply slips in the x direction, whereas

in second case the same ply slips this time in the y

• direction. The respective solutions will be called

P1(x,y) and P2(x,y). The linear solution could be written like:

1 2

( . ( , ) . ( , )),

x y

P V P x y V P x y η = +

• (4)

Where V= (Vx, Vy) is the velocity vector, The pressure gradient is calculated:

1 2 1 2

. . . . . ,

x y x y

gradP V gradP V gradP gradP e gradP e V M V η η η η = +

• =

⊗ + ⊗ ⋅

• =

⋅ ⋅

• (5)

Where,

1 2 x y

M gradP e gradP e = ⊗ + ⊗

• Integrating the shear stress over the sliding surface

allows calculating the friction force:

1 2 1 2 , 1 2 1 2 ,

( , ) ( ) 2 ( ) 2 .

x y x y x y f

F x y dxdy h h V grad P dxdy h h h h M I dxdy V h h C V τ η η

→ → →

= + = − + −

• +

= − + ⋅

• −
• =
• (6)

This model predicts the friction force Ff as a function of the friction matrix Cf and velocity V. The friction matrix Cf depends on both plies geometries, described by h1 and h2, and on the pressure gradient. 2.1 Model Analyses The previous model shows that the coefficient of friction is not scalar according to the velocity. After calculating Eigen values 1, 2 and their corresponding Eigen vectors u1 and u2, of matrix Cf , we deduced that friction force is only collinear to velocity when this one is collinear to u1 or u2 vectors.

1 1 1 2 2 2

.( . ) .( . ) F u F u λ β λ β = =

• (7)

1, 2, u1 and u2 depend on the film thickness, distribution and regularity. Fig.2. Schematic representation of friction force when velocity is collinear with u1 or u2 3 Numerical results and discussion The previously presented model (equ.6) was applied to calculate friction parameters between two 3×3 Twill plies as shown in (Fig. 2). Geometric equations of both plies are given by:

* 1 1 1 * 2 2 2

2 2 ( , ) 1 cos cos 2 2 ( , ) 1 cos cos

x y x y

x y h x y h T T x y h x y h T T π π ε π π ε

• =

+ ⋅

• =

− ⋅

• (8)

x y u2 u1 F1 F2

Fig.3. Inter-ply slip between two 3x3 Twill plies The maximum and the minimum film thicknesses are equal to:

* * max 1 1 2 2 * * min 1 1 2 2

(1 ) (1 ) (1 ) (1 ) e h h e h h ε ε ε ε = + − − = − + +

(9) As h1

*, h2 *, 1, 2, Tx, Ty and N, the number of

collocation points, are the imposed values (Table 1), P1(x,y), P2(x,y), and their respective gradients could now be calculated using the pseudo-spectral Fourier

• method. Profiles are shown in (Fig. 4).

Table 1. Example Parameters Parameter Value Unit

h1

*

12.10-6 m

h2

*

6.10-6 m 1 0.2 2 0.2

Tx

0.06 m

Ty

0.06 m

• 100

Pa.s

N

15

Fig.4. Different pressure and gradient of pressure profiles

1 2 3 4 5 6 2 4 6 0.4 0.6 0.8 1 1.2 1.4 1.6 x 10

• 3

x (cm) y (cm) Z(x,y) (cm)

2 4 6 8 2 4 6 8

• 1
• 0.5

0.5 1 x 10

8

x (cm) y (cm) P1(x,y) (Pa)

2 4 6 8 2 4 6 8

• 1
• 0.5

0.5 1 x 10

8

x (cm) y (cm) P2(x,y) (Pa)

2 4 6 8 2 4 6 8

• 2
• 1

1 2 x 10

5

x (cm) y (cm) dP1/dx (N/m)

2 4 6 8 2 4 6 8

• 3
• 2
• 1

1 2 x 10

5

x (cm) y (cm) dP1/dy (N/m)

2 4 6 8 2 4 6 8

• 3
• 2
• 1

1 2 x 10

5

x (cm) y (cm) dP2/dx (N/m)

2 4 6 8 2 4 6 8

• 2
• 1

1 2 x 10

5

x (cm) y (cm) dP2/dy (N/m)

3.1 Influence of film thickness on friction behavior As demonstrated before, the friction matrix Cf, which characterize the relation between friction force and velocity, is dependant from both plies geometries h1 and h2. Or in other terms, the thickness of resin film layer formed between both plies will play an important role in the variation of the components of Cf. To evaluate this influence, we calculated Cf for different (emin/emax) values. Fig.5 shows that changing film thickness did not affect the Eigen vectors. In our case, when the velocity vector is deflected by a ±45° angle with x- axis, friction force is collinear to this vector whatever the film thickness variation is.

Fig.5. Eigen values and Eigen vectors of Cf function of

(emin/emax) On the other hand, the irregularity of film thickness has a significant effect on 1 and 2. With the increase

• f (emin/emax) values 1 and 2 will finish by being

equal (Fig. 6).

Fig.6. Variation of anisotropy factor with film irregularity

4 Conclusions The inter-ply slip is very variable, and plays an important role in forming processes of thermoplastic

• laminates. Modeling this phenomenon shows that the

coefficient of friction is not scalar according to the

• velocity. Variation in film thickness has a significant

effect on relation between friction force and velocity. 5 Acknowledgements This work was introduced and financed by the Technical Center

• f

Mechanical engineering industries (CETIM). The authors are anxious to thank the partners of the pole IPC (Engineering of polymers and composites). References

[1] Chen, julie. (2000) Stamping of continous fiber thermoplastic composites., polymer composites. [2] Hou, M. and Friedrich, K. (1994) 3-D stamp forming

• f

thermoplastic matrix composites. Applied composite Materials., Vols. pp.135-153. [3] Trudel-Boucher. (2005) Experimental investigation of stamp forming of unconsolidated commingled E- glass/polypropylene fibrics, Composites science and technology. [4] A.M. Murtagh, M.R. Monoghan and P.J. Mallon. (1994) , Investigation of the Interply Slip Process in

• Continuous. Madrid : s.n., Proceedings of ICCM 9.

[5] Murtagh, Adrian M. (1995) , Shear Characterisation of unidirectional and fabric reinforced thermoplastic composites for pressforming applications. Canada : s.n., ICCM 10. [6] K. Vanclooster, S.V. Lomov and I. Verpoest., (2008), Investigation of interply shear in composite forming. [7] Gorczyca-Cole Jennifer, James A. Sherwood, Julie

• Chen. (2006), A friction model for thermostamping

commingled glass-polypropylen woven fabrics. Composites Part A: applied science and manufacturing. [8] L.Gamache, J. A. Sherwood, J. Chen and J. Cao. (2007),.Characterisation

• f

fabric/tool and fabric/fabric friction during the thermostamping

• process. Proceedings of the tenth Esaform Conference
• n Material Forming.

[9] R.Akkerman, M.P. Ubbink, M.B.de Rooij and R.H.W. ten Thije. (2007),.Tool-ply friction in composite

• forming. Esaform.

[10] Konstantine A. Fetfatsidis, James A. Sherwood, Julie Chen and David Jauffres. (2009), Characterization of the fabric/Tool and fabric/fabric friction during thermostamping process. Esaform.

• 2000
• 1500
• 1000
• 500

500 1000 1500 2000

• 2000
• 1500
• 1000
• 500

500 1000 1500 2000 emin/emax 0.05 0.07 0.1 0.125 0.166 0.25 0.5

x y

1

u

• 2

u

• 0.6

0.7 0.8 0.9 1 0.05 0.2 0.35 0.5 2 / 1 emin / emax